Wellfoundedness proofs by means of non-monotonic inductive definitions I: Π₂⁰-operators

Journal of Symbolic Logic 69 (3):830-850 (2004)
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Abstract

In this paper, we prove the wellfoundedness of recursive notation systems for reflecting ordinals up to Π₃-reflection by relevant inductive definitions

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10.2178/jsl/1096901770

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Citations of this work

Proof theory of weak compactness.Toshiyasu Arai - 2013 - Journal of Mathematical Logic 13 (1):1350003.
Proof theory for theories of ordinals II:< i> Π_< sub> 3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1):39-92.
Epsilon substitution method for [Π0 1, Π0 1]-FIX.T. Arai - 2005 - Archive for Mathematical Logic 44 (8):1009-1043.
Reading Gentzen's Three Consistency Proofs Uniformly.Ryota Akiyoshi & Yuta Takahashi - 2013 - Journal of the Japan Association for Philosophy of Science 41 (1):1-22.

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References found in this work

Laforte, G., see Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):287.
Proof theory for theories of ordinals—I: recursively Mahlo ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
Ordinal diagrams for recursively Mahlo universes.Toshiyasu Arai - 2000 - Archive for Mathematical Logic 39 (5):353-391.

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